Question:
The LCM and product of two numbers X and Y are 180 and 2700, respectively. If X is completely divisible by Y, then the value of (X-Y) is _____.
The LCM and product of two numbers X and Y are 180 and 2700, respectively. If X is completely divisible by Y, then the value of (X-Y) is _____.
Updated On: Aug 31, 2024
- 132
- 195
- 180
- 165
- 182
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The Correct Option is D
Solution and Explanation
HCF of X and Y =\(\frac{product}{LCM}=\frac{2700}{180}=15\)
Let Y = 15a and given X is completely divisible by Y, then
X = 15ab
For HCF of X and Y to be 15, a must be 1.
So, X = 15b and Y = 15
Now, product of two numbers = 2700
15b × 15 = 2700
⇒ b = 12
So, (X – Y) = 15(12 – 1) = 15 × 11 = 165.
So, The correct option is (D) : 165.
Let Y = 15a and given X is completely divisible by Y, then
X = 15ab
For HCF of X and Y to be 15, a must be 1.
So, X = 15b and Y = 15
Now, product of two numbers = 2700
15b × 15 = 2700
⇒ b = 12
So, (X – Y) = 15(12 – 1) = 15 × 11 = 165.
So, The correct option is (D) : 165.
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